A q-deformed Aufbau Prinzip

Négadi, Tidjani; Kibler, M.

doi:10.1088/0305-4470/25/4/002

Cited by 24 publications

(19 citation statements)

References 21 publications

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“…[16] Kibler, of l'Universite Claude Bernard Lyon I, has shown how group theory undergirds atomic and fundamental-particle periodicity [17,18] and how q-deformed groups reproduce the shell structures of neutral atoms, of positive ions, and of hydrogen-like ions depending on the value of q. [19] …”

Section: Discussionmentioning

confidence: 99%

Why do molecules echo atomic periodicity?

Hefferlin¹,

Sackett²,

Tatum

2013

Int. J. Quantum Chem.

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Franck-Condon factors are investigated for sequences of free main-group diatomic molecules. Theory-based Condon loci (parabolas) and Morse-potential loci are plotted on Deslandres tables to verify if they, indeed, follow the largest Franck-Condon factors. Then, the inclination angles of the Condon loci are determined. Thus, entire band systems are quantified by one variable, the angle. For all available isoelectronic sequences, this angle increases from a central minimum toward magic-number molecular boundaries. The theory for the Condon locus gives the angle in terms of the ratio of the upper-state to the lowerstate force constants. It is concluded that the periodicity is caused due to the fact that this ratio becomes larger as rare-gas molecules are approached, a trend that probably points to the extreme cases of the rare-gas molecules themselves. Thus, molecular periodicity echoes atomic periodicity in that data plots have extrema at molecules with magic-number atoms, yet it does not echo the details of atomic periodicity in series between those molecules.

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Section: Discussionmentioning

confidence: 99%

Why do molecules echo atomic periodicity?

Hefferlin¹,

Sackett²,

Tatum

2013

Int. J. Quantum Chem.

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“…A similar correct Aufbau rule holds for free atoms: If an atom has two energetically near-degenerate valence levels, the upper one becomes populated, too, if its energy distance is smaller than the difference of the respective electron repulsion energies (e.g. Pilar, 1968;Ne´gadi and Kibler, 1992;Melrose and Scerri, 1996;Mann et al, 2000). The oversimplified version of the Aufbau rule, ''The lowest energy orbitals are filled at first'', only holds for orbital level schemes with large gaps, i.e.…”

Section: Filling Order Of Atomic Valence Orbitalsmentioning

confidence: 90%

Recommended Questions on the Road towards a Scientific Explanation of the Periodic System of Chemical Elements with the Help of the Concepts of Quantum Physics

Schwarz

2006

Found Chem

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Periodic tables (PTs) are the 'ultimate paper tools' of general and inorganic chemistry. There are three fields of open questions concerning the relation between PTs and physics: (i) the relation between the chemical facts and the concept of a periodic system (PS) of chemical elements (CEs) as represented by PTs; (ii) the internal structure of the PS; (iii) The relation between the PS and atomistic quantum chemistry. The main open questions refer to (i). The fuzziness of the concepts of chemical properties and of chemical similarities of the CE and their compounds guarantees the autonomy of chemistry. We distinguish between CEs, Elemental Stuffs and Elemental Atoms. We comment on the basic properties of the basic elements. Concerning (ii), two sharp physical numbers (nuclear charge and number of valence electrons) and two coarse fuzzy ranges (ranges of energies and of spatial extensions of the atomic orbitals, AOs) characterize the atoms of the CEs and determine the two-dimensional structure of the PS. Concerning (iii), some relevant 'facts' about and from quantum chemistry are reviewed and compared with common 'textbook facts'. What counts in chemistry is the whole set of nondiffuse orbitals in low-energy average configurations of chemically bonded atoms. Decisive for the periodicity are the energy gaps between the core and valence shells. Diffuse Rydberg orbitals and minute spin-orbit splittings are important in spectroscopy and for philosophers, but less so in chemical science and for the PS.

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“…In many of these works, tuning the parameter q to a given value, or to several given values, from an infinity of ones (q a real or complex number), could describe in an improved way the considered physical system, describing subtle effects. For example, starting from a mathematical formula for the spectrum of the hydrogen atom and introducing a q-deformation, we obtained the construction principle for the neutral atoms, positive ions, etc., [21]. As another example, the q-deformations have been linked to the smooth (non-linear) behavior of phenomena in atomic nuclei [22].…”

Section: Summary and Concluding Remarksmentioning

confidence: 99%

The Genetic Codes: Mathematical Formulae and an Inverse Symmetry-Information Relationship

Négadi

2016

Information

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First, mathematical formulae faithfully describing the distributions of amino acids and codons and reproducing the degeneracies in the various known genetic codes, including the standard genetic code, are constructed, by hand. Second, we summarize another mathematical approach relying on the use of q-deformations to describe these same genetic codes, and add a new application not considered before. Third, by considering these same genetic codes, we find, qualitatively, that an inverse symmetry-information relationship exists.

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A q-deformed Aufbau Prinzip

Abstract: Abstract. A building principle working for both atoms and monoatomic ions is proposed in this Letter. This principle relies on the q-deformed "chain" SO(4) > SO(3) q .

Cited by 24 publications

References 21 publications

Why do molecules echo atomic periodicity?

Why do molecules echo atomic periodicity?

Recommended Questions on the Road towards a Scientific Explanation of the Periodic System of Chemical Elements with the Help of the Concepts of Quantum Physics

The Genetic Codes: Mathematical Formulae and an Inverse Symmetry-Information Relationship

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